Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
weighted Bloch spaces; projection; inverse mapping; dual space
weighted Bloch spaces; projection; inverse mapping; dual space
Summary:
This work is an introduction to anisotropic spaces of holomorphic functions, which have $\omega$-weight and are generalizations of Bloch spaces on a unit ball. We describe the holomorphic Bloch space in terms of the corresponding $L_\omega ^\infty $ space. We establish a description of $(A^p(\omega ))^*$ via the Bloch classes for all $0<p\leq 1$.
References:
[1] Attele R.: Bounded analytic functions and the little Bloch space. Internat. J. Math. Math. Sci. 13 (1990), no. 1, 193--198. DOI 10.1155/S016117129000028X | MR 1038664 | Zbl 0701.30045
[2] Anderson J.M.: Bloch function: The basic theory. Operators and Function Theory (Lancaster, 1984), Reidel, Dordrecht, 1985, pp. 1--17. MR 0810441
[3] Arazy J.: Multipliers of Bloch functions. University of Haifa, Mathematics Publication Series 54, 1982.
[4] Bishop C.J.: Bounded functions in the little Bloch space. Pacific J. Math. 142 (1990), no. 2, 209--225. DOI 10.2140/pjm.1990.142.209 | MR 1042042 | Zbl 0652.30024
[5] Djrbashian A.E., Shamoian F.A.: Topics in the theory of $ A^p_{\alpha }$ spaces. Teubner Texts in Math., 105, Teubner, Leipzig, 1988. MR 1021691 | Zbl 0667.30032
[6] Djrbashian M.M.: On the representation problem of analytic functions. Soobsh. Inst. Matem. Mekh. Akad. Nauk Armyan. SSR 2 (1948), 3--40.
[7] Harutyunyan A.V.: Bloch spaces of holomorphic functions in the polydisc. J. Funct. Spaces Appl. 5 (2007), no. 3, 213--230. DOI 10.1155/2007/353959 | MR 2352842
[8] Nowak M.: Bloch space on the unit ball of $ C^n$. Ann. Acad. Sci. Fenn. Math. 23 (1998), no. 2, 461--473. MR 1642142
[9] Rudin W.: Function Theory in the Unit Ball of $ C^n$. Springer, New York, Heidelberg, Berlin, 1980. MR 0601594
[10] Seneta E.: Functions of Regular Variation. (in Russian), Nauka, Moscow, 1985.
[11] Yang W.: Some characterizations of $\alpha$-Bloch spaces on the unit ball of $ C\sp n$. Acta Math. Sci. (English Ed.) 17 (1997), no. 4, 471--477. MR 1613263
[12] Zhu K.: Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics, 226, Springer, New York, 2005. MR 2115155 | Zbl 1067.32005
[13] Zhou Z.: The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications. 2005, arXiv: math.Fa/0503723v3. Zbl 1131.47021
Search
Partner of
